Speaker: Yichen Ma, Cornell University
Title: Enumeration of flags in partial orders and convex geometries
Time: 2:30 PM, Monday, March 11, 2024
Place: Malott 206
Abstract: We consider a Hopf monoid of partial orders and another of
convex geometries, and investigate combinatorial invariants
constructed from characters on them. Each invariant comes in a pair
consisting of a polynomial and a (more general) quasisymmetric
For partial orders we obtain the order polynomial of Stanley and the
enriched order polynomial of Stembridge. For convex geometries we
obtain polynomials first introduced by Edelman-Jamison and
Billera-Hsiao-Provan. We obtain reciprocity results satisfied by these
polynomials from the perspective of characters in a unified manner.
We describe the coefficients of the quasisymmetric invariants as
enumerating faces on certain simplicial complexes. These include the
barycentric subdivision of the CW-sphere of a convex geometry.
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